{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ML_in_Finance_ARIMA-HFT\n",
    "# Author: Matthew Dixon\n",
    "# Version: 1.0 (24.7.2019)\n",
    "# License: MIT\n",
    "# Email: matthew.dixon@iit.edu\n",
    "# Notes: tested on Mac OS X with Python 3.6 and Tensorflow 1.3.0\n",
    "# Citation: Please cite the following reference if this notebook is used for research purposes:\n",
    "# Dixon M.F., I. Halperin and P. Bilokon, Machine Learning in Finance: From Theory to Practice, Springer Graduate textbook Series, 2020. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview\n",
    "The purpose of this notebook is to demonstrate the application of ARIMA time series modeling to high frequency data. The model predicts changes in the VWAP (volume weighted average prices) based on historical observations of the VWMAP and an exogenous variable, the current Order Flow Imbalance (OFI). See https://arxiv.org/abs/1011.6402 for more details on OFI.\n",
    "\n",
    "The notebook describes many of the steps in Chapter 6 on applying the Dickey-Fuller test to establish stationarity of the endogenous series, followed by use of the ACF and PACF to identify the ARIMA model order. Typically, addition diagnostic tests are performed on the model residual but omitted here. Instead we simply compare the forecast with the actual VWAP change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
      "  import pandas.util.testing as tm\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "from ofi import ofi, time_as_index, smart_price\n",
    "from statsmodels.regression.linear_model import OLS\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (12, 9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sp500quotes = pd.read_pickle('../data/09012013_quotes.pickle')\n",
    "time_as_index(sp500quotes)\n",
    "\n",
    "sp500ofi = ofi(sp500quotes['Bid Size'], sp500quotes['Ask Size'],\n",
    "               sp500quotes['Bid Price'], sp500quotes['Ask Price'])\n",
    "sp500smart = smart_price(sp500quotes['Bid Price'], sp500quotes['Bid Size'], \n",
    "                         sp500quotes['Ask Price'], sp500quotes['Ask Size'])\n",
    "\n",
    "sp500smart_diff = sp500smart.diff(1)\n",
    "pd.concat([sp500ofi, sp500smart_diff], axis=1).plot(kind='scatter', \n",
    "                                                    x='OFI', y='VWAP', alpha=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stationarity\n",
    "It is essential to determine whether the time series is \"stationary\". Informally, stationarity is when the auto-covariance is independent of time. Failure to establish stationarity will almost certainly lead to misinterpretation of model identification and diagnostics tests. Moreover, stationarity is decisive in characterizing the prediction problem and whether to use a more advanced architecture. In particular, we can expect a plain RNN to perform poorly if the data is non-stationary as the RNN exhibits fixed auto-covariance. \n",
    "\n",
    "We perform an Augmented Dickey-Fuller test to establish stationarity under the assumption that the time series has a constant bias but does not exhibit a time trend. In other words, we assume that the time series is already de-trended. \n",
    "\n",
    "If the stationarity test fails, even after first de-trending the time series, then one potential recourse is to simply take differences of time series and predict $\\Delta y_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The null hypothesis of the Augmented Dickey-Fuller is that there is a unit root, with the alternative that there is no unit root. If the p-value is above $(1-\\alpha)$, then we cannot reject that there is a unit root. Note that a subset of the time series is used to reduce the computation time of the test. Test separately on both the dependent and the independent variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample = sp500smart_diff[1:]\n",
    "adf, p, usedlag, nobs, cvs, aic = sm.tsa.stattools.adfuller(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF: -51.65350270603796\n",
      "p-value: 0.0,\n",
      "N: 82102, \n",
      "critical values: {'1%': -3.4304296509764045, '5%': -2.861575204399113, '10%': -2.566788738084499}\n"
     ]
    }
   ],
   "source": [
    "adf_results_string = 'ADF: {}\\np-value: {},\\nN: {}, \\ncritical values: {}'\n",
    "print(adf_results_string.format(adf, p, nobs, cvs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reject the Null hypothesis at the 99% level - the difference in smart prices contain no unit roots and are stationary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determine the order p of the AR model from the PACF plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Autoregressive Model Identification: The partial auto-correlation\n",
    "It is important to determine the number of lags, the sequence length, required in the RNN by statistical analysis. A brute-force approach will in general be too time-consuming.\n",
    "\n",
    "A partial auto-correlation at lag $h\\geq 2$ is a conditional auto-correlation between a variable, $X_t$, and its $h^{th}$ lag, $X_{t-h}$ under the assumption that we control for the values of the intermediate lags, $X_{t-1},\\dots, X_{t-h+1}$:\n",
    "\n",
    "$$\\begin{align}\\tau_h&:=\\tau(X_t, X_{t-h}; X_{t-1},\\dots, X_{t-h+1})\\\\\n",
    "&:=\\frac{\\gamma(X_t, X_{t-h}; X_{t-1},\\dots, X_{t-h+1})}{\\sqrt{\\gamma(X_t |X_{t-1},\\dots, X_{t-h+1})\\gamma(X_{t-h} |X_{t-1},\\dots, X_{t-h+1}))}}\n",
    ",\\end{align}$$\n",
    "where $\\gamma_h:=\\gamma(X_tX_{t-h})$ is the lag-$h$ autocovariance. The partial autocorrelation function $\\tau_h:\\mathbb{N} \\rightarrow [-1,1]$ is a map $h:\\mapsto \\tau_h$.\n",
    "\n",
    "The estimated partial auto-correlation function (PACF) can be used to identify the order of an autoregressive time series model. Values of $|\\tau_h|$ greater or equal to $\\frac{\\Phi^{-1}(\\alpha)}{\\sqrt{T}}$, where $T$ is the number of observations and $\\Phi(z)$ is the standard normal CDF, are significant lag $h$ partial autocorelations at the $\\alpha$ confidence level.\n",
    "\n",
    "We use the stattools package to estimat the PACF. The `nlags` parameter is the maximum number of lags used for PACF estimation of the endogeneous variable - SP500 mid-prices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "pacf = sm.tsa.stattools.pacf(sp500smart_diff[1:], nlags=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since $\\Phi^{-1}(0.99) \\simeq 2.58$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = len(sp500smart_diff)\n",
    "\n",
    "sig_test = lambda tau_h: np.abs(tau_h) > 2.58/np.sqrt(T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find the first lag which isn't significant at the 99% level and automatically determine the number of lags needed in our autoregressive model as one below this value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p set to 17\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(pacf)):\n",
    "    if sig_test(pacf[i]) == False:\n",
    "        p = i - 1\n",
    "        print('p set to', p)\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This may lead to a high order model, with more lags than strictly necessary. We could view this value, informally, as an upper bound on the number of lags needed. We can also simply identify the order of the model based on the plot of the PACF. In this case, a minimum of approximately 10 lags appears satisfactory, although more may be needed.  We plot the PACF function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pacf, label='pacf')\n",
    "plt.plot([2.58/np.sqrt(T)]*30, label='99% confidence interval (upper)')\n",
    "plt.plot([-2.58/np.sqrt(T)]*30, label='99% confidence interval (lower)')\n",
    "plt.xlabel('number of lags')\n",
    "plt.xticks(np.arange(0, 30, 2))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determine the order $q$ of the MA model from the ACF plot\n",
    "Evaluate the ACF on the endogenous variable - SP500 mid-prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/statsmodels/tsa/stattools.py:541: FutureWarning: fft=True will become the default in a future version of statsmodels. To suppress this warning, explicitly set fft=False.\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "acf = sm.tsa.stattools.acf(sp500smart_diff[1:], nlags=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = len(sp500smart)\n",
    "\n",
    "sig_test = lambda tau_h: np.abs(tau_h) > 2.58/np.sqrt(T)\n",
    "\n",
    "q = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q set to 8\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(acf)):\n",
    "    if sig_test(acf[i]) == False:\n",
    "        q = i - 1\n",
    "        print('q set to', q)\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(acf, label='acf')\n",
    "plt.plot([2.58/np.sqrt(T)]*30, label='99% confidence interval (upper)')\n",
    "plt.plot([-2.58/np.sqrt(T)]*30, label='99% confidence interval (lower)')\n",
    "plt.xlabel('number of lags')\n",
    "plt.xticks(np.arange(0,30,2))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "train on the first 10,000 samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/statsmodels/tsa/base/tsa_model.py:219: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
      "  ' ignored when e.g. forecasting.', ValueWarning)\n"
     ]
    }
   ],
   "source": [
    "n_train = 10000\n",
    "p = 10\n",
    "model = sm.tsa.ARIMA(endog=sp500smart_diff[1:(n_train+1)], \n",
    "                     order=(p, 0, q), exog=sp500ofi[0:n_train])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/statsmodels/base/model.py:492: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/statsmodels/base/model.py:512: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  \"Check mle_retvals\", ConvergenceWarning)\n"
     ]
    }
   ],
   "source": [
    "model_fit = model.fit(disp=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/statsmodels/tsa/arima_model.py:1441: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(np.diag(-inv(hess)))\n",
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:903: RuntimeWarning: invalid value encountered in greater\n",
      "  return (a < x) & (x < b)\n",
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:903: RuntimeWarning: invalid value encountered in less\n",
      "  return (a < x) & (x < b)\n",
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1912: RuntimeWarning: invalid value encountered in less_equal\n",
      "  cond2 = cond0 & (x <= _a)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>VWAP</td>       <th>  No. Observations:  </th>    <td>10000</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(10, 8)</td>   <th>  Log Likelihood     </th>  <td>9235.095</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>    <td>0.096</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 28 May 2020</td> <th>  AIC                </th> <td>-18428.190</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>13:02:07</td>     <th>  BIC                </th> <td>-18276.772</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>                <td>0</td>        <th>  HQIC               </th> <td>-18376.936</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                       <td> </td>        <th>                     </th>      <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>       <td>    0.0002</td> <td>    0.000</td> <td>    0.719</td> <td> 0.472</td> <td>   -0.000</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>OFI</th>         <td>    0.0006</td> <td> 2.29e-05</td> <td>   24.093</td> <td> 0.000</td> <td>    0.001</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.VWAP</th>  <td>   -0.0505</td> <td>    0.214</td> <td>   -0.236</td> <td> 0.814</td> <td>   -0.470</td> <td>    0.369</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.VWAP</th>  <td>    0.4020</td> <td>    0.194</td> <td>    2.070</td> <td> 0.038</td> <td>    0.021</td> <td>    0.783</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3.VWAP</th>  <td>    0.4948</td> <td>    0.203</td> <td>    2.436</td> <td> 0.015</td> <td>    0.097</td> <td>    0.893</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4.VWAP</th>  <td>   -0.2672</td> <td>    0.600</td> <td>   -0.446</td> <td> 0.656</td> <td>   -1.443</td> <td>    0.908</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L5.VWAP</th>  <td>   -0.3877</td> <td>    0.143</td> <td>   -2.705</td> <td> 0.007</td> <td>   -0.669</td> <td>   -0.107</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L6.VWAP</th>  <td>   -0.1725</td> <td>    0.349</td> <td>   -0.495</td> <td> 0.621</td> <td>   -0.856</td> <td>    0.511</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L7.VWAP</th>  <td>    0.3912</td> <td>    0.240</td> <td>    1.629</td> <td> 0.103</td> <td>   -0.079</td> <td>    0.862</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L8.VWAP</th>  <td>   -0.0159</td> <td>    0.117</td> <td>   -0.136</td> <td> 0.892</td> <td>   -0.246</td> <td>    0.214</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L9.VWAP</th>  <td>   -0.0007</td> <td>    0.013</td> <td>   -0.055</td> <td> 0.956</td> <td>   -0.027</td> <td>    0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L10.VWAP</th> <td>   -0.0502</td> <td>    0.011</td> <td>   -4.434</td> <td> 0.000</td> <td>   -0.072</td> <td>   -0.028</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.VWAP</th>  <td>   -0.1451</td> <td>    0.215</td> <td>   -0.676</td> <td> 0.499</td> <td>   -0.566</td> <td>    0.276</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.VWAP</th>  <td>   -0.5515</td> <td>    0.140</td> <td>   -3.942</td> <td> 0.000</td> <td>   -0.826</td> <td>   -0.277</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.VWAP</th>  <td>   -0.5018</td> <td>    0.280</td> <td>   -1.795</td> <td> 0.073</td> <td>   -1.050</td> <td>    0.046</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L4.VWAP</th>  <td>    0.3357</td> <td>    0.583</td> <td>    0.576</td> <td> 0.565</td> <td>   -0.807</td> <td>    1.479</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L5.VWAP</th>  <td>    0.3639</td> <td>      nan</td> <td>      nan</td> <td>   nan</td> <td>      nan</td> <td>      nan</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L6.VWAP</th>  <td>    0.0997</td> <td>    0.451</td> <td>    0.221</td> <td> 0.825</td> <td>   -0.783</td> <td>    0.983</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L7.VWAP</th>  <td>   -0.4640</td> <td>    0.270</td> <td>   -1.718</td> <td> 0.086</td> <td>   -0.993</td> <td>    0.065</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L8.VWAP</th>  <td>    0.0352</td> <td>    0.150</td> <td>    0.235</td> <td> 0.814</td> <td>   -0.259</td> <td>    0.329</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>    <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th>  <td>          -0.9838</td> <td>          -0.4982j</td> <td>           1.1028</td> <td>          -0.4254</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th>  <td>          -0.9838</td> <td>          +0.4982j</td> <td>           1.1028</td> <td>           0.4254</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.3</th>  <td>          -0.4090</td> <td>          -1.0372j</td> <td>           1.1149</td> <td>          -0.3098</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.4</th>  <td>          -0.4090</td> <td>          +1.0372j</td> <td>           1.1149</td> <td>           0.3098</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.5</th>  <td>           0.9763</td> <td>          -0.7222j</td> <td>           1.2143</td> <td>          -0.1014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.6</th>  <td>           0.9763</td> <td>          +0.7222j</td> <td>           1.2143</td> <td>           0.1014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.7</th>  <td>           1.3953</td> <td>          -0.3335j</td> <td>           1.4346</td> <td>          -0.0373</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.8</th>  <td>           1.3953</td> <td>          +0.3335j</td> <td>           1.4346</td> <td>           0.0373</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.9</th>  <td>          -0.9861</td> <td>          -1.8350j</td> <td>           2.0832</td> <td>          -0.3285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.10</th> <td>          -0.9861</td> <td>          +1.8350j</td> <td>           2.0832</td> <td>           0.3285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th>  <td>          -0.9722</td> <td>          -0.5168j</td> <td>           1.1010</td> <td>          -0.4222</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th>  <td>          -0.9722</td> <td>          +0.5168j</td> <td>           1.1010</td> <td>           0.4222</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th>  <td>          -0.4022</td> <td>          -1.0249j</td> <td>           1.1010</td> <td>          -0.3095</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.4</th>  <td>          -0.4022</td> <td>          +1.0249j</td> <td>           1.1010</td> <td>           0.3095</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.5</th>  <td>           1.0754</td> <td>          -0.0000j</td> <td>           1.0754</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.6</th>  <td>           0.9796</td> <td>          -0.6593j</td> <td>           1.1808</td> <td>          -0.0943</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.7</th>  <td>           0.9796</td> <td>          +0.6593j</td> <td>           1.1808</td> <td>           0.0943</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.8</th>  <td>          12.8807</td> <td>          -0.0000j</td> <td>          12.8807</td> <td>          -0.0000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                   VWAP   No. Observations:                10000\n",
       "Model:                    ARMA(10, 8)   Log Likelihood                9235.095\n",
       "Method:                       css-mle   S.D. of innovations              0.096\n",
       "Date:                Thu, 28 May 2020   AIC                         -18428.190\n",
       "Time:                        13:02:07   BIC                         -18276.772\n",
       "Sample:                             0   HQIC                        -18376.936\n",
       "                                                                              \n",
       "===============================================================================\n",
       "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "const           0.0002      0.000      0.719      0.472      -0.000       0.001\n",
       "OFI             0.0006   2.29e-05     24.093      0.000       0.001       0.001\n",
       "ar.L1.VWAP     -0.0505      0.214     -0.236      0.814      -0.470       0.369\n",
       "ar.L2.VWAP      0.4020      0.194      2.070      0.038       0.021       0.783\n",
       "ar.L3.VWAP      0.4948      0.203      2.436      0.015       0.097       0.893\n",
       "ar.L4.VWAP     -0.2672      0.600     -0.446      0.656      -1.443       0.908\n",
       "ar.L5.VWAP     -0.3877      0.143     -2.705      0.007      -0.669      -0.107\n",
       "ar.L6.VWAP     -0.1725      0.349     -0.495      0.621      -0.856       0.511\n",
       "ar.L7.VWAP      0.3912      0.240      1.629      0.103      -0.079       0.862\n",
       "ar.L8.VWAP     -0.0159      0.117     -0.136      0.892      -0.246       0.214\n",
       "ar.L9.VWAP     -0.0007      0.013     -0.055      0.956      -0.027       0.025\n",
       "ar.L10.VWAP    -0.0502      0.011     -4.434      0.000      -0.072      -0.028\n",
       "ma.L1.VWAP     -0.1451      0.215     -0.676      0.499      -0.566       0.276\n",
       "ma.L2.VWAP     -0.5515      0.140     -3.942      0.000      -0.826      -0.277\n",
       "ma.L3.VWAP     -0.5018      0.280     -1.795      0.073      -1.050       0.046\n",
       "ma.L4.VWAP      0.3357      0.583      0.576      0.565      -0.807       1.479\n",
       "ma.L5.VWAP      0.3639        nan        nan        nan         nan         nan\n",
       "ma.L6.VWAP      0.0997      0.451      0.221      0.825      -0.783       0.983\n",
       "ma.L7.VWAP     -0.4640      0.270     -1.718      0.086      -0.993       0.065\n",
       "ma.L8.VWAP      0.0352      0.150      0.235      0.814      -0.259       0.329\n",
       "                                    Roots                                     \n",
       "==============================================================================\n",
       "                   Real          Imaginary           Modulus         Frequency\n",
       "------------------------------------------------------------------------------\n",
       "AR.1            -0.9838           -0.4982j            1.1028           -0.4254\n",
       "AR.2            -0.9838           +0.4982j            1.1028            0.4254\n",
       "AR.3            -0.4090           -1.0372j            1.1149           -0.3098\n",
       "AR.4            -0.4090           +1.0372j            1.1149            0.3098\n",
       "AR.5             0.9763           -0.7222j            1.2143           -0.1014\n",
       "AR.6             0.9763           +0.7222j            1.2143            0.1014\n",
       "AR.7             1.3953           -0.3335j            1.4346           -0.0373\n",
       "AR.8             1.3953           +0.3335j            1.4346            0.0373\n",
       "AR.9            -0.9861           -1.8350j            2.0832           -0.3285\n",
       "AR.10           -0.9861           +1.8350j            2.0832            0.3285\n",
       "MA.1            -0.9722           -0.5168j            1.1010           -0.4222\n",
       "MA.2            -0.9722           +0.5168j            1.1010            0.4222\n",
       "MA.3            -0.4022           -1.0249j            1.1010           -0.3095\n",
       "MA.4            -0.4022           +1.0249j            1.1010            0.3095\n",
       "MA.5             1.0754           -0.0000j            1.0754           -0.0000\n",
       "MA.6             0.9796           -0.6593j            1.1808           -0.0943\n",
       "MA.7             0.9796           +0.6593j            1.1808            0.0943\n",
       "MA.8            12.8807           -0.0000j           12.8807           -0.0000\n",
       "------------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_fit.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/dez/miniconda3/envs/MLFenv/lib/python3.6/site-packages/statsmodels/tsa/base/tsa_model.py:576: ValueWarning: No supported index is available. Prediction results will be given with an integer index beginning at `start`.\n",
      "  ValueWarning)\n"
     ]
    }
   ],
   "source": [
    "start_index = n_train\n",
    "horizon = 500\n",
    "end_index = start_index + horizon\n",
    "forecast = model_fit.predict(start=start_index, end=end_index, exog=sp500ofi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "forecast.index = sp500smart_diff[n_train:n_train + horizon + 1].index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sp500smart_diff[n_train:(n_train + horizon + 1)], color='black', label='Delta VWAP')\n",
    "plt.plot(forecast, color='blue', label='forecast')\n",
    "plt.title('Forecast of VWAP changes versus Actual')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('delta VWAP')\n",
    "plt.legend();"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
